Magnetic resonance imaging (MRI) is a common and well known technique for imaging the internal structure of objects and for medical diagnosis. MRI requires that the object to be imaged be placed in a uniform (typically to within 1 ppm) and strong (typically in the range of 0.5 to 1.5 Tesla) magnetic field.
Magnetic resonance imaging also requires gradient fields for altering slightly the strong, homogeneous field as a function of location. For 3-dimensional imaging, switched gradient fields must be provided in the X, Y and Z directions. Specially designed gradient coils are used to provide the gradient fields. One gradient coil is required for each dimension, so for 3-dimensional imaging, 3 gradient coils are needed.
Typically, the gradient coils are located within the bore of the homogeneous magnet and around the object to be imaged. This places certain geometrical constraints on the shape and size of the gradient coils. For imaging the spine, for example, the gradient coil must fit around the body. For imaging the head, the gradient coil must fit around the head. Typically, gradient coils are located on a cylindrical surface or biplanar surface. However, this may not be the best shape for many body parts. Some body parts are obviously not cylindrical and it may be better to have a gradient coil that more closely resembles the shape of the body part to be imaged. In the present state of the art, there exist a few methods for designing gradient coils constrained to arbitrarily shaped surfaces. Conjugate gradient descent and simulated annealing are two examples. However, these gradient coil design methods tend to be slow computationally. It would be an advance in the art to provide a method for designing gradient coils on arbitrarily shaped surfaces that is computationally faster.
Homogeneous magnets have a certain `field of view` (FOV) where the homogeneous magnetic field is suitable for magnetic resonance imaging. Similarly, gradient coils have an FOV where the gradient field is suitable for imaging. Imaging can only be provided in a volume where the homogeneous magnet FOV and gradient coil FOV overlap. Some homogeneous magnets have a FOV which is substantially nonspherical (e.g. an oblate or prolate spheroid). In such cases it is best for the FOV of the gradient coil to closely match the FOV of the homogeneous magnet. However, in the present state of the art, it is not clear how to efficiently design gradient coils having a FOV of arbitrary shape.
Furthermore, in the present state of the art it is not clear how to simultaneously provide the features of fast computation speed, an ability to design on arbitrarily shaped surfaces, and an ability to provide an arbitrarily shaped FOV. It would be an advance in the art of MRI and magnet design to provide a method which provides all these desirable features simultaneously.